The Gauss Map of a Genus Three Theta Divisor

Clint McCrory, Theodore Shifrin, Robert Varley
1992 Transactions of the American Mathematical Society  
A smooth complex curve is determined by the Gauss map of the theta divisor of the Jacobian variety of the curve. The Gauss map is invariant with respect to the (-l)-map of the Jacobian. We show that for a generic genus three curve the Gauss map is locally Z/2-stable. One method of proof is to analyze the first-order Z/2-deformations of the Gauss map of a hyperelliptic theta divisor.
doi:10.2307/2154137 fatcat:5nwpntb67nco7bsk6hjeftsqau